You have most thoroughly misunderstood the position of women's rights campaigners opposing self-identification of legal sex. Assuming that you wish to engage with us, I'll address a few of your points.
By saying "you can't be a woman if you're born without a vagina, and if you're born with a vagina you must be a woman" you're making reproductive organs the defining and most important characteristic of being a woman.
It's a good thing then that we are neither saying that nor believe it.
A woman is an adult human female. A female human is someone who has a female body with a reproductive system geared towards producing large gametes (ova). Humans with this type of reproductive system are grouped together as the female sex class. Membership of this class does not depend on the reproductive system of a female-bodied individual being complete or fully functional. But it does depend on meeting a very small number of defining characteristics. In both biology and UK law, these characteristics are gonads, genitals and chromosomes. Typically, anyone who is born with two out of three of these characteristics (ovaries, vulva, XX-chromosomes) will be classified as female.
This attitude was used to oppress women for centuries. We were baby makers only, and hormonal and chromosomal differences were used to say that we were too "emotional " for public life, education and jobs.
We have been oppressed on the basis of our sex for rather longer than a few centuries. And it had nothing to do with having a vagina, which is not after all, readily visible, but with the reproductive capacity those born with a vulva are assumed to have.
Being born female has material consequences for how we are treated by society, how we are raised, how we are expected to behave and present ourselves and how we may live our lives.
From its very beginnings, feminism has criticised and opposed these expectations and limitations imposed upon female people on the basis of their sex. Women's rights campaigners who oppose self-identification are no different.
The attitude that has oppressed us isn't the one that says "you can't be a woman if you're born without a vagina, and if you're born with a vagina you must be a woman". If that was true, we could have ended our oppression thousands of years ago. But our oppression isn't definitional, it doesn't arise from the fact that we are called women if we have a vulva. It arises from the fact that only those born with a vulva can bear offspring. Whatever they are named.
You cannot make this go away by including some female-bodied and male-bodied people in the opposite sex class. But you can obscure the root of our oppression and you can prevent it from being addressed by rendering sex invisible.
In other words, insisting that the oppressed class within a system that disadvantages people because of their (assumed and real) reproductive capacity to bear offspring cannot be defined and recognised as a class on the basis of having this capacity is a move that benefits only the oppressor class. If we cannot name the root cause of this oppression, we cannot address it.
Everything that happens to women and girls to keep them oppressed in patriarchal systems arises from this one, basic fact of our species: We are the sex class that bears offspring.
We are saying that this basic fact does not justify the way we are treated in patriarchal societies. We are saying that this basic fact of our biology does not define what other things we can do and be and wear and like. Female people can like and wear and do all kinds of things that male people do. Not just things our society has coded as feminine.
This is why we oppose the doctrine of gender identity which posits that your membership of a sex class depends on your behaviour or how you feel.
To put it another way, take doing the dishes and mowing the lawn
A conservative may say:
It's the woman's job to cook dinner.
It's the man's job to mow the lawn.
A proponent of gender identity puts forward this view:
Whoever cooks dinner is the woman.
Whoever mows the lawn is the man.
A feminist would say:
Both men and women can do either of those jobs. Sex is irrelevant here.
Gender is not a set of stereotypes - it's an identity based on culture, history, society , psychology and often (but not always) sex.
Across time and space, the sex stereotypes and sex role stereotypes imposed on either sex may differ but they shape culture, history and society. What you call gender identity is something that I understand as a personality based on an individual's preference for or rejection of any number and combination of the stereotypes that their society and culture imposes on either sex.
The definition of gender as the straitjacket that society tries to force us in from birth, so that we comply with the sex stereotypes and sex role stereotypes our culture associates with our sex is a feminist definition. Part of that definition is that because of the hierarchical nature of these sex stereotypes and sex role stereotypes which typically frames masculine-coded ones in a positive way and feminine-coded ones in a positive way, we also understand that the female sex class suffers more from gender than the male sex class. Hence we say that sex is the root of our oppression and gender is the tool used to oppress us. And that is true whether we comply or defy - most of the stereotypes associated with the female sex class serve to hold us back and gender-non-conformity in women is punished in many if not most societies.
It's far more freeing than "vagina = woman" and takes account of each of us as individuals not just bodies, which is what feminism up until now has fought for.
May I suggest you extend your feminist reading? Various strands of feminism focus on women as a class, and it is liberal feminism which emphasises the individual. Liberal feminism does not aim to abolish the patriarchy but instead seeks to help each individual woman navigate the patriarchal system she lives in to her best advantage. It does not focus on class-based analysis of the issues and work towards broad, systemic change, but it tinkers around the edges instead. There is a lot of focus on symptoms not root causes of women and girls being disadvantaged.
That's not to say that liberal feminists embracing the doctrine of gender identity didn't fight for and achieve some improvements for women and girls. They did. Liberal feminists chose to work with and within the system and that can be an effective tactic on any issue.
But now, they are actively opposing the aims of radical feminists, who want to liberate all females from patriarchal oppression, not help some women make the best of it.